The manufacturing of integrated circuits in high volumes relies on lithography to define the features printed on the semiconductor chips. The lithography process starts first by coating the surface of the semiconductor wafer with a radiation-sensitive material called a photo-resist or resist. An image of a mask is projected onto the resist and the resist is subsequently developed to create a resist pattern on a wafer. A source of radiation is shone through the mask in the case of a transparent mask. Transparent masks are mostly used in optical lithography with typical wavelengths of 436 nm, 405 nm, 365 nm, 248 nm, 193 nm and possible future wavelengths of 157 nm, and 126 nm. Transparent masks made of opaque regions and clear regions are referred to as binary masks. Alternatively transparent masks can be made of a partially transparent layer patterned to define clear and partially transparent regions to the radiation. The optical properties of the partially transparent material, namely its complex refractive index and its thickness, are chosen to adjust the phase and transmission of the light going through the partially transparent material as compared to the phase and the transmission of the light going through the clear regions of the mask.
As the feature size decreases in comparison to the exposure wavelength, distortion in the pattern transfer process becomes more severe and the quality of the image is drastically altered, essentially due to the properties of light, and the fact that the wavelength of light becomes significant relative to feature size and mask thickness for very small patterns.
Many different approaches have been used in order to correct for these effects including the use of proximity effect correction, phase shifting masks, inverse lithography, off-axis illumination, customized illumination and source-mask optimization. These techniques typically rely on the use of accurate lithography modeling in order to assess the improvement of the image or generate a corrected mask layout or a corrected source distribution.
One approach to lithography modeling is based on the fact that the source can be considered a spatially incoherent collection of independent sources. Each source point gives an image according to coherent imaging. The total image is the incoherent addition of the individual images for each source point. Each source point has a corresponding propagation direction of the light impinging on the mask. This method is usually referred as the “source integration method.” The intensity on the wafer is the sum of the intensity computed for each source point. For a given source point the Fourier transform of the mask is computed and only the mask diffraction orders going through the lens pupil are taken into account to compute the image. Accurate results can be obtained but the overall computation is slow due to the need to compute the mask diffraction spectrum and due to the reconstruction of the image for each source point.
Another approach is based on the calculation of the transmission cross coefficients (TCC), which describes a four dimensional low pass filter applied to the spatial frequencies of the mask and of its complex conjugate. An advantage of the TCC calculation is that the TCC can be computed once for a given exposure tool and reused for different mask layouts as long as the mask layout size is the same. A Singular Value Decomposition (SVD) is applied to a TCC matrix, and the resulting “Kernels” can be convolved directly to the mask pattern to generate a wafer image. As eigenvalues of the SVD decay rapidly, only the first few Kernels are used to compute the images with sufficient accuracy. As the convolution is a linear operation, the mask can be decomposed into simpler shapes and the convolutions to simpler shapes can be pre-computed and stored in look-up tables. The calculation of the image is then performed by using the look-up table results.
The TCC technique offers the advantage that it is efficient in terms of speed, but often at the expense of accuracy; the TCC technique relies on a number of approximations and it is not well suited for applications where the parameters of the optical system need to be changed like for example custom illumination and source-mask illumination, (the TCC typically must be recomputed for each new illuminator). On the other hand, the source integration method is quite accurate and flexible but it is too slow to be used for very large computations like for example proximity effect correction of a large chip or inverse lithography.
What is needed is a simulation method that combines speed, accuracy and flexibility, and an associated way to make semiconductor masks that are more accurate and that cost less to develop. Such a method could potentially substantially reduce the cost of semiconductor design, and ultimately, semiconductor manufacture. The present invention satisfies these needs and provides further, related advantages.